@plbrault I went with backtracking for several hours too. Finding any possible solution wasn't too bad on most, but proving the impossible ones on an np-hard should have been my clue.

Worst part is I'd filtered the regions by impossible areas already as the first step. 😅

@adw99 Sorry for the delay. Something like this?

from itertools import product

list1 = list('ABC')
list2 = list(range(1,6))

print(list(product(*[product(list1[i],list2) for i in range(3)])))

@3j0hn Yeah, I cleaned the list that way in minutes and then spent hours on my backtrack solver and visualizations for combining shapes using Minkowski/etc.

Finding any solution was easy. Proving _impossible_ scenarios like the test case should have been the obvious clue; but I was too deep down the rabbit hole by then.

Since I used nx.topological_sort() to do the heavy lifting for me on this one, here's an implementation of Kahn's algorithm to do the same thing for any graph model.

https://github.com/jstanden/advent-of-code-python/blob/main/2025/journals/topological-sort-graph.ipynb

@JesseSkinner Thanks! I haven't tried to write a linear solver yet, but it would be a fun challenge after AoC.

I always go straight for z3 and have a better appreciation for what it's doing now.

For Day 11's penance for using networkx, I'll probably implement topological sort with BFS. 😅